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Karen Yeats
Asymptotic Density in Combined Number Systems
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| Published: |
April 12, 2002
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| Keywords: |
additive number system, multiplicative number system, asymptotic density, partition set, ratio test, regular variation |
| Subject: |
Primary 11N45, 11P99, Secondary 05A16, 11N80 |
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Abstract
Necessary and sufficient conditions are found for
a combination of additive number systems and a combination of
multiplicative number systems to preserve the property
that all partition sets have asymptotic density.
These results cover and extend
several special cases mentioned in the literature
and give partial solutions to two problems in [6].
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| Acknowledgements
Thanks to Stan Burris, a patient and meticulous supervisor, to the referee for his interest and detailed comments, and to NSERC for their Undergraduate Student Research Award which supported this research.
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| Author information
Department of Pure Mathematics, University of Waterloo, Waterloo Ontario, N2L 3G1, Canada
kayeats@uwaterloo.ca
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